# Limit l'hopital's

1. Mar 4, 2013

### whatlifeforme

1. The problem statement, all variables and given/known data
evaluate the limit

2. Relevant equations
lim k->∞ (1+r/k)^k

3. The attempt at a solution
1. lim k->∞ ln(1+rk^-1) / (k^-1)

not sure how to get to this next step:

2. lim k->∞ (-rk^-2)/(1+rk^-1) / -k^-2

not sure how to get to this next step:

3. lim k->∞ r/(1+rk^-1)

not sure how to get to this next step:

4. lim k->∞ rk/k+r

not sure how to get to this next step:

5. lim k->∞ r/1 = r

6. lim k->∞ (1+r/k)^k

7. lim k->∞ f(k) = lim k->∞ e^lnf(k) = e^r

2. Mar 4, 2013

### Dick

After you take the log take the derivative of the numerator and denominator, like you usually do with l'Hopital. Use the chain rule. What do you get?

3. Mar 4, 2013

### LCKurtz

If you don't understand each step, how did you do each step? Or are you trying to follow someone else's work? Do you have the limit definition of $e$ to work with?$$e = lim_{n\rightarrow \infty}\left(1 + \frac 1 n\right)^n$$If so, there is no need for L'Hospital's rule. Try the substitution $k = ru$.